Does this telescoping series converge or diverge? if it converges, what is the sum?

Question

 

∑ ((n/n+1) - (n+2/n+3)) = ?

 

converges to -5/6

 

how do you cancel out the terms to find the sum?

Answer 1

∑((n/n+1)-(n+2/n+3))=∑(1/(n+3)-1/(n + 1))

S_n=-(13n+5m2)/(6(n+1)(n+3))-->-5/6